w2 example 1 answers

1a Write an equation that can be used to work out the

volume of water entering the basin without knowing the

volume of water leaving the basin.

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

• Then rearrange for V1:

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

• Then rearrange for V1:

V1S1 = V1S2 +WS2

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

• Then rearrange for V1:

V1S1 = V1S2 +WS2

V1S1 − V1S2 = WS2

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

• Then rearrange for V1:

V1S1 = V1S2 +WS2

V1S1 − V1S2 = WS2

V1 S1 − S2 = WS2

1a • Substitute V2 in the second equation with its equivalent from the first

equation:

V1S1 = (V1 +W)S2

• Then rearrange for V1:

V1S1 = V1S2 +WS2

V1S1 − V1S2 = WS2

V1 S1 − S2 = WS2

𝐕𝟏 =𝐖𝐒𝟐

𝐒𝟏 − 𝐒𝟐

1b It is important to be able to calculate the additions to the

water also without knowing the volume of water leaving

the basin. Write an equation to do this.

1b • Rearrange your previous equation to make W the subject:

1b • Rearrange your previous equation to make W the subject:

V1 =WS2

S1 − S2

1b • Rearrange your previous equation to make W the subject:

V1 =WS2

S1 − S2

V1 S1 − S2 = WS2

1b • Rearrange your previous equation to make W the subject:

V1 =WS2

S1 − S2

V1 S1 − S2 = WS2

𝐕𝟏 𝐒𝟏 − 𝐒𝟐𝐒𝟐

= 𝐖

1c Over a year, a lagoon of surface area 50m2 gains 1.12m

of water by precipitation and 0.81m by run-off, but loses

1.26m by evaporation. What is W for the lake in m3s-1?

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

P = 1.12my−1 =1.12 x 50

31536000= 1.78 x 10−6m3s−1

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

P = 1.12my−1 =1.12 x 50

31536000= 1.78 x 10−6m3s−1

R = 0.81my−1 =0.81 x 50

31536000= 1.28 x 10−6m3s−1

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

P = 1.12my−1 =1.12 x 50

31536000= 1.78 x 10−6m3s−1

R = 0.81my−1 =0.81 x 50

31536000= 1.28 x 10−6m3s−1

E = 1.26my−1 =1.26 x 50

31536000= 2.00 x 10−6m3s−1

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

P = 1.12my−1 =1.12 x 50

31536000= 1.78 x 10−6m3s−1

R = 0.81my−1 =0.81 x 50

31536000= 1.28 x 10−6m3s−1

E = 1.26my−1 =1.26 x 50

31536000= 2.00 x 10−6m3s−1

• Put the converted P, R and E back into the equation for W:

1c • To convert m/year into m3s-1, you need to multiply it by the area if the

basin and divide by the number of seconds in a year:

1 year = 356 x 24 x 60 x 60 seconds = 31536000s

P = 1.12my−1 =1.12 x 50

31536000= 1.78 x 10−6m3s−1

R = 0.81my−1 =0.81 x 50

31536000= 1.28 x 10−6m3s−1

E = 1.26my−1 =1.26 x 50

31536000= 2.00 x 10−6m3s−1

• Put the converted P, R and E back into the equation for W:

W = 1.78 + 1.28 − 2 x 106m3s−1 = 𝟏. 𝟎𝟔 𝐱 𝟏𝟎−𝟔𝐦𝟑𝐬−𝟏

1d Seawater of salinity 35 seeps into the lagoon at a rate of

5.4 x 10-5m3s-1 which has a salinity of exactly 35. What

will the salinity of the lagoon be after at least a year?

1d • Substitute V2 in the second equation with its equivalent from

the first equation:

1d • Substitute V2 in the second equation with its equivalent from

the first equation:

V1S1 = (V1 +W)S2

1d • Substitute V2 in the second equation with its equivalent from

the first equation:

V1S1 = (V1 +W)S2

• Rearrange for S2 and substitute in the values you know:

1d • Substitute V2 in the second equation with its equivalent from

the first equation:

V1S1 = (V1 +W)S2

• Rearrange for S2 and substitute in the values you know:

V1S1(V1 +W)

= S2

1d • Substitute V2 in the second equation with its equivalent from

the first equation:

V1S1 = (V1 +W)S2

• Rearrange for S2 and substitute in the values you know:

V1S1(V1 +W)

= S2

S2 =5.4 x 10−5 x 35

5.4 x 10−5 + 1.06 x 10−6= 𝟑𝟒. 𝟑𝟑